Eevee has severe frame-rate drops with animated objects that have normal maps on them. The problem has been reported and can be viewed with a nice sample file here:
https://developer.blender.org/T64458
This Addon replaces Normal Map Nodes in Blender to improve EEVEE Viewport Performance. The performance gains are significant.
This is based on this idea by pcanback: https://blenderartists.org/t/way-faster-normal-map-node-for-realtime-animation-playback-with-tangent-space-normals/1175379
I am only maintaining this add-on, the heavy lifting was done by anonymous persons and BeheadedKamikaze https://github.com/BeheadedKamikaze